Document Type: Original Article
Authors
^{1} Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
^{2} Department of Mechanical Engineering, Pardis Branch, Islamic Azad University, Pardis, Iran
^{3} Department of Mechanical Engineering, Imam Khomeini International University, Qazvin, Iran
Abstract
Keywords
1. Introduction
Nowadays, a large number of refrigeration systems use mechanical compression that is energyintensive. Nevertheless, there is a growing concern about conventional refrigeration system operating fluids which contribute to the destruction of the ozone layer, greenhouse effects, and global warming. Improvement of refrigeration systems more economically and more environmentallyfriendly is one of the alternative options to tackle these challenges. Recently, there has been a growing attention in research to improve the absorption refrigeration systems (ARSs) (Kaynakli and Kilic, 2007). This system is a possible choice for using the remaining heat and renewable resources such as geothermal and solar energies (Soltani et al., 2019a, 2019b). The use of renewable and abundant solar radiation is suggested as an appropriate substitute. Recently, solar chillers may represent a suitable alternative for water and gas air conditioners, which consume electricity to a large extent. Moreover, the working fluids of these processes are compatible with the environment (Sun et al., 2012). Although the overall cooling effect per unit of supplied energy performance of the ARS is usually low, the remaining heat such as the one rejected from power plants may be used to increase the global energy utilization (McQuiston et al., 2004).
In the absorption refrigeration cycle, the required heat for the generator is supplied by solar energy. In order to run the working fluid in absorption chillers, thermal energy is used, which may be supplied through steam, hot water resulting from direct combustion of fuel, or through solar energy. Many researchers have worked on the doubleeffect H_{2}OLiBr ARS by performing energy, exergy, and economic analyses (Kaushik and Arora, 2009; Kaynakli et al., 2015; Gomri, 2009; Talukdar and Gogoe, 2016, Morosuk and Tsatsaronis, 2008; Misra et al., 2005; Bereche et al., 2009). One main characteristic of the doubleeffect ARSs is its capability to work in parallel, series, and reverse parallel flow configurations with respect to the operating solution flow via the heat exchangers and generators (Arun et al., 2000, 2001; Garousi Farshi et al., 2011, 2012). Liu and Wang (2004) studied the performance of a LiBrH_{2}O gas/solar doubleeffect ARS. In their intended system, the highpressure generator is run by conventional energy, natural gas, and solar energy. Results indicated that this system is economically feasible and efficient. MoleroVillar et al. (2012) carried out a comparison between solarpowered ARSs to select the most appropriate condition of cooling systems containing solar energy. Boudéhenn et al. (2012) investigated the LiBrH_{2}O absorption chiller system equipped with a solar energy collector. Sun et al. (2015) studied a gas/solar absorption cooling and heating system in a commercial building. Results indicated that 49.7% saving is achieved in the consumption of gas using this system. Mussati et al. (2018) investigated the configuration optimization of series flow doubleeffect LiBrH_{2}O ARSs by minimizing the costs. Razmi et al. (2018) presented a system that works by hybridization of an ideal vapor compression system with a singleeffect absorption system.
Performance analysis and thermodynamic modeling of ARSs are common in the study of vapor absorption cooling research. Performance of doubleeffect ARSs have been assessed in the literature (Garousi Farshi et al., 2011, 2012; Talpada and Ramana, 2019; Kaushik et al., 2018; Lima et al., 2019; Sioud et al., 2018). A comprehensive review of vapor ARSs and hybrid ARSs is performed for solar cooling applications by Kaushik et al. (Kaushik et al., 2018). The thermodynamic model developed for a prototype absorption chiller using NH_{3}/LiNO_{3 }is investigated by Lima et al. (2019). Recently, Sioud et al. (2018) investigated the feasibility and the eventual improvement in the performance of an ejector powered LiBrH_{2}O doubleeffect absorption/recompression refrigeration cycle driven by hightemperature heat sources.
Given the high consumption of absorption chillers and the amount of power and energy required in the generator of the system, evaluating the savings in gas consumption by employing a solar collector, as an alternative solution, can be very useful and needs to be further investigated. The present study will address the effect of employing solar energy on fuel consumption of series and parallel twostage ARSs. First, two intended systems are designed and then, the COPs of the refrigeration system and also power consumption are calculated by connecting the solar collector to the ARS. In the following, the impact of varying the evaporator temperature on the COP of the system will be studied. A thermodynamic analysis of the system is conducted and the internal variables such as pressure and temperature of different components including the condenser and the evaporator are calculated.
2. Mathematical Modeling
2.1. System Description
The main components of twostage absorption chillers include evaporator, absorber, hightemperature generator (HTG), lowtemperature generator (LTG), condenser, steam and liquid separator, hightemperature heat exchanger (HTHX), lowtemperature heat exchanger (LTHX), lowtemperature soluble pump, soluble pump, and refrigerant pump. In absorption cycles, the efficiency of refrigeration equipment is assessed using the COP. Figs. 1 and 2 respectively illustrate a schematic of the parallel and series doubleeffect absorption chillers with the absorber soluble of LiBr. These cycles have an evaporator, an HTG absorber, an LTG, two heat exchangers, and two condensers. In the series cycle, an outlet dilute soluble from the absorber is pumped into an LTHX, and is then let into an HTHX and afterward directly into a HTG. However, in the parallel cycle, this dilute soluble is injected into the LTG and the HTG simultaneously, the evaporated water enters the condensers and the concentrated soluble returns the absorber as in the series cycle. In both series and parallel cycles, the evaporated water taken from the LiBrH_{2}O solution enters a distinct condenser in each generator.
Figure 1. LiBrH_{2}O doubleeffect cycle of the parallel type
Figure 2. LiBrH_{2}O doubleeffect cycle of the series type
The schematics of the modeled system are shown in Figs.1 and 2. The system is composed of two generators, one absorber, two condensers, one evaporator, two pumps, two expansion valves, and two heat exchangers. As demonstrated by Fig. 1, the system has five temperature values (for LTG, HTG, hightemperature condenser (HTC), condenser, and absorber), and three pressure levels (low pressure in the evaporator and the absorber, medium pressure in the condenser and LTG, and high pressure in HTG and HTC).
The term “doubleeffect” refers to the fact that the inlet heat is used twice in the cycle of vapor production at high temperatures. The generated vapor is used as the inlet heat in the HTG. This vapor, then, enters the hightemperature, where phasechange or condensation occurs due to loss of heat. This heat is high enough to move vapor out of the heat exchanger in the LTG. Therefore, the heat is utilized twice and demonstrates double effects.
One of the main options of designing in doubleeffect technology for increasing the COP is the selection method of the flow connections. The major options for this case are the series and the parallel types of flows. The cycle demonstrated in Fig. 1 is drawn with the assumptions of parallel flow and also the same change in mass fraction of each generator. Fig. 2 illustrates a schematic of the series flow, where the flow in this direction first enters the HTG and then the LTG. In both cases, the process of internal heat exchange between the HTC and the LTG restricts the temperature. The HTC must have a high enough temperature for heat transfer to LTG.
2.2. System Modeling
The cycle has been modeled using the equations of energy and mass balance, for each component. The outlet mass flow rate of absorber is denoted by .In general, it is expected that the flow rate at the upper circuit (pump 2) be specified. Yet, the energy balance equation between the HTC and the lowtemperature one is utilized to calculate the higher flow rate. The heat exchanger’s mass flow rate is specified in four foreign heat transfer loops. As the initial temperature of each loop is specified, the value of is assumed the input data for each of the external heat exchangers. This value is also considered for the condenser ( ). The assumptions and the considered inputs are similar to the parallel flow model.
2.2.1. Assumptions of the Problem
To model the doubleeffect of the ARS, several assumptions are considered as the following:
1 The system and the heat exchanger are under steadystate conditions.
2 At the condenser outlet, water is a saturated liquid.
3 At the evaporator outlet, water is a saturated vapor.
4 LiBr’s temperature at the absorber outlet is the absorber’s temperature.
5 The outlet heat temperature of the absorber and the generator depends on the balance conditions of mixing and separation.
6 Heat loss and pressure drop in the tubes and heat exchangers have been ignored.
7 Heat exchange between the system and the environment does not occur except in the HPG, the evaporator, the condenser, and the absorber.
8 In default conditions of system, water is operated with a temperature of 25 ℃ and pressure of 1 atm.
2.3. Thermodynamic Analysis
The equations and the first and second laws of thermodynamics are taken into consideration in this section. The first law of thermodynamics defines energy transfer, while the second law describes the quality of energy and material. In order to conduct thermodynamic analysis of the ARS, the mass equation, and the first and second laws of thermodynamics have been applied to each component of the system equipment.
Mass equations including the mass balance governing the whole cycle and conservation of concentration equation under steadystate flow and steadystate system conditions are as follows:
(1) 

(2) 
where and X denote mass flow rate and mass concentration of LiBr, respectively. These equations are written for chiller components of the parallel and series cycles.
The first law of thermodynamics demonstrates the energy balance equation for each component, and it is stated as follows:
(3) 
where Q denotes the value of the heat transfer between the control volume of system and its surrounding environment, and W is the positive work amount of system. Energy balance for components of these systems in parallel doubleeffect conditions is presented as Table 1. It is noteworthy that the equations of the doubleeffect series system components are also similar to these equations.
The overall performance of energy in refrigeration cycles is demonstrated using the COP, which is defined as follows:
(4) 
In this study, EES software version 9.4 was used for data analysis and sensitivity analysis. Conducting the calculations related to the first and second laws of thermodynamics, thermal efficiency, component equations, and other thermodynamic and mathematical calculations are achieved by programming in EES.
Table 1. Energy balance equations for different components in doubleeffect series and parallel systems
Components 
Equations 
HTG 

LTHX 

HTHX 

HTC 

Condenser 

Evaporator 

Absorber 

LTG and HTC 
3. Results and Discussion
This section analyzes and compares the results obtained from the simulation. After presenting the obtained results and sensitivity analysis of different parameters, the bestoperating conditions are selected for the system. First, to examine the accuracy of the calculations, the results of the present simulation for the COP have been compared with the work of Gomri (2009) in Fig. 3. The results of this comparison have indicated a completely desirable match between the two studies. Results of the simulation including the system’s thermodynamic properties are shown for the series and parallel cycles in Table 2. Other specifications including the system’s COP, the pump’s power consumption, the heat transfer rate of each component, and the heat exchanger’s efficiency are presented in Table 3.
Figure 3. Verification of the results of the current study with the study of Gomri (2009) for the conditions of T_{con}=360K & T_{eva}=277K
Table 2. Thermodynamic specifications of the parallel and series flow cycles
Parallel flow 

Series flow 

Point 
T (℃) 
(kg/s) 
X (%) 
h (J/g) 
s (J/g K) 
Point 
T (℃) 
(kg/s) 
X (%) 
h (J/g) 
s (J/g K) 

1 
29.78 
1.00 
52.613 
65.0 
0.203 
1 
29.89 
1 
52.839 
65.9 
0.2029 

2 
29.78 
1.00 
52.613 
65.0 
0.203 
2 
29.89 
1 
52.839 
65.9 
0.2029 

3 
54.41 
1.00 
52.613 
117.5 
0.366 
3 
57.45 
1 
52.839 
124.4 
0.3844 

4 
76.81 
0.85 
61.921 
195.6 
0.427 
4 
78.98 
0.844 
62.615 
203 
0.434 

5 
43.89 
0.85 
61.921 
133.9 
0.244 
5 
44.62 
0.844 
62.615 
139.3 
0.2461 

6 
47.29 
0.85 
61.921 
133.9 
0.264 
6 
48.38 
0.844 
62.615 
139.3 
0.2675 

7 
57.69 
0.067 
0 
2,607.6 
8.613 
7 
58.66 
0.074 
0 
2,609.4 
8.605 

8 
30.14 
0.15 
0 
126.2 
0.4384 
8 
30.63 
0.156 
0 
128.3 
0.4453 

9 
5.3 
0.15 
0 
126.2 
9.016 
9 
5.05 
0.156 
0 
128.3 
9.022 

10 
5.3 
0.15 
0 
2,510.3 
9.016 
10 
5.04 
0.156 
0 
2,509.8 
9.022 

11 
57.69 
0.55 
52.613 
124.5 
0.387 
11 
 
 
 
 
 

12 
57.71 
0.55 
52.613 
124.5 
0.388 
12 
 
 
 
 
 

13 
103.47 
0.55 
52.613 
222.4 
0.664 
13 
107.46 
1 
52.839 
231.1 
0.6842 

14 
145.42 
0.46 
61.921 
324.3 
0.765 
14 
140.29 
0.918 
57.554 
304.5 
0.7965 

15 
84.02 
0.46 
61.921 
209.1 
0.465 
15 
82.3 
0.918 
57.554 
188.3 
0.4917 

16 
77.45 
0.46 
61.921 
209.1 
0.430 
16 
69.11 
0.918 
57.554 
188.3 
0.4165 

17 
123.17 
0.08 
0 
2,725.9 
7.683 
17 
129.68 
0.082 
0 
2,737.4 
7.619 

18 
88.31 
0.08 
0 
369.8 
1.173 
18 
93.68 
0.082 
0 
392.4 
1.235 

19 
30.14 
0.083 
0 
369.8 
1.242 
19 
30.63 
0.082 
0 
392.4 
1.315 

20 
150.00 
8,000 
0 
2,746.4 
6.838 
20 
150.00 
8 
0 
2,746.4 
6.838 

21 
142.40 
8,000 
0 
599.6 
1.764 
21 
141.88 
8 
0 
597.3 
1.759 

22 
25.00 
12,000 
0 
104.8 
0.367 
22 
25.00 
12 
0 
104.8 
0.367 

23 
33.45 
12,000 
0 
140.1 
0.4839 
23 
33.80 
12 
0 
141.6 
0.4886 

24 
25.00 
12,000 
0 
104.8 
0.367 
24 
25.00 
12 
0 
104.8 
0.367 

25 
28.72 
12,000 
0 
120.3 
0.418 
25 
29.08 
12 
0 
121.8 
0.4238 

26 
12.00 
20,000 
0 
50.4 
0.180 
26 
12.00 
20 
0 
50.4 
0.1804 

27 
7.73 
20,000 
0 
32.5 
0.117 
27 
7.57 
20 
0 
31.8 
0.1149 
The assumption in this system is that the maximum mass ratio must be smaller than the point where crystallization occurs because this occurrence is not desired for the system. In other words, this requirement is an assumption made to simplify the modeling.
In the following, by changing the absorber’s outlet flow rate, variations in the value of the system’s COP may be observed for both cycles. Fig. 4 presents the variations in COP versus the absorber outlet flow rate. The COP of the parallel flow is higher than the series flow; however, the reduction of the system’s COP by increasing the absorber’s outlet mass flow rate is similar in both of the cycles. On the other hand, although the COP of the series flow cycle is smaller than that of the parallel flow, it is of higher capacity.
Table 3. Specifications of different components of the cycle in both the parallel and the series flows
Parameter 
Parallel flow 
Series flow 
Unit 
COP 
1.404 
1.363 
 
Eff_{LHX} 
70 
70 
% 
Eff_{HHX} 
70 
70 
% 
UA_{LHX} 
2.923 
3.266 
[kW/K] 
UA_{HHX} 
1.61 
3.723 
[kW/K] 
UA_{eva} 
85 
85 
[kW/K] 
UA_{abs} 
50 
50 
[kW/K] 
UA_{cd} 
65 
65 
[kW/K] 
UA_{HTC} 
10 
10 
[kW/K] 
UA_{HTG} 
25 
25 
[kW/K] 
Q_{cd,,in} 
195.263 
192.109 
[kW] 
Q_{abs} 
426.059 
443.517 
[kW] 
Q_{cd,out} 
187.566 
205.742 
[kW] 
Q_{eva} 
358.386 
371.708 
[kW] 
Q_{HTG} 
225.215 
272.719 
[kW] 
Q_{LHX} 
52.429 
58.511 
[kW] 
Q_{HHX} 
53.971 
106.715 
[kW] 
Q_{Tot} 
1,713 
1,843 
[kW] 
W_{Pump 1} 
0.002 
0.002 
[kW] 
W_{Pump 2} 
0.022 
 
[kW] 
The overall heat transfer value has been investigated in Fig.5. This figure studies variations of the overall heat transfer with respect to the absorber’s outlet flow rate for both of the series and the parallel flows. As the results demonstrate, it may be observed that an increase in the overall exchanged heat in terms of the absorber’s outlet flow rate is not linear, and the increasing slope is decreased at higher flow rates.
The results of Fig.6 indicate that the COP is better in the parallel cycle than in series one. As is observed, with an assumption of 280 K temperature for the evaporator, the COP of the parallel cycle is always higher at all temperature levels of the highpressure generator than that of the series cycle. Furthermore, it was observed at other temperature levels considered for the evaporator that increasing the temperature in the highpressure generator results in increasing COP. However, the rate of increase in COP at initial temperatures of the highpressure generator (range of 390420 K) was higher, and as the temperature increases (range of 420470 K), the rate of increase in COP reduces. The parallel cycle has consistently shown a better performance than the series cycle.
Figure 4. Variations in COP in terms of the outlet flow rate of the absorber
Figure 5. The amount of total exchanged heat with respect to the absorber’s outlet flow rate
Figure 6. The effect of the evaporator’s and the generator’s temperatures on COP
Figure 7. The impact of the condenser’s and the generator’s temperatures on COP
Fig. 7 shows variations of the cycle’s COP with respect to the variations in the temperature of the condenser as well as the generator’s temperature on the cycle. Results demonstrated the superiority of the parallel cycle’s COP to the series one.
In Fig.8, other parameters including the evaporator and the generator’s temperature variations to the pressure have been investigated. It may be observed that pressure variations in the series cycle are intensively increasing, while such variations in the parallel cycle are insignificant compared to the series cycle. This shows that the parallel cycle is more reliable than series one.
Figure 8. The impact of the evaporator’s and the generator’s temperatures on the pressure of the highpressure generator
Fig.9 provides investigation of variations in the generator’s pressure by changing the temperature of the condenser and the generator. As is observed, with an increase in the condenser’s temperature in the parallel cycle, variations of pressure at various temperatures are different but insignificant. However, in the series cycle, such variations are almost equal at different temperatures, but pressure variations are intensively increased.
It may be observed in Fig.10 that increasing the efficiency of highand LTHXs would change COP in the series and the parallel cycles. With an increase in the efficiency of HTHX, the parallel cycle COP is higher than that of the series. Also, in LTHX, with an increase in efficiency, the parallel cycle COP is higher than that of the series. This fact, by itself, indicates the superiority of the parallel cycle to the series one with respect to efficiency in HTHX and LTHXs.
Figure 9. The impact of the condenser’s and the generator’s temperatures on the pressure of HPG
Figure 10. The effect of HTHE and LTHXs on COP
6. Conclusion
The purpose of examining two parallel and series cycles in the present study is the optimization of the system. In refrigeration cycles, unlike in other cycles, the capability of the system’s performance is studied through COP. It should be noted that this procedure is similar in waterammonia fluid, and only the working fluid changes. On the other hand, the efficiency and COP of LiBr systems are always greater than those of ammonia. Therefore, to optimize the system, different comparisons have been made between the series and the parallel cycles by analyzing the LiBrH_{2}O system. Results demonstrated that the parallel cycle with LiBrH_{2}O working fluid has a higher COP than the series cycle. Thus, the proposed LiBrH_{2}O parallel cycle model may be utilized in order to optimize the system. The inlet heat source in the present work is supplied by solar energy, which is assumed as an inlet heat source with a specified flow rate and temperature in the results and analyses. This value may be reduced or increased to optimize consumption in the system with the best COP, the fact which is directly related to fuel consumption. In other words, considering different uses and applications, temperatures, and conditions, these assumptions may vary. Thus, the amount of fuel consumption or the energy source will also change. In conclusion, it may be stated that the performance of the first and the second laws of thermodynamics of the parallel cycle is better than that of the series. As a result, this leads to a reduction of fuel consumption significantly. Furthermore, the parallel cycle with the mentioned conditions is efficient due to having the best COP and performance. The heat transfer in the evaporator, the absorber, the condenser, HTG, HTHX, and LTHX is lower in the parallel cycle than in the series one. However, in the parallel cycle, the heat transfer for the HTC is higher than that of the series cycle.
Nomenclature
ARS 
Absorption refrigeration systems 
COP 
Coefficient of performance 
Eff 
Efficiency 
HTC 
High temperature condenser 
HTG 
Hightemperature generator 
HTHX 
Hightemperature heat exchanger 
h 
Enthalpy (J/g) 
LTG 
Lowtemperature generator 
LTHX 
Lowtemperature heat exchanger 
Mass flow rate (kg/s) 

Q 
Heat transfer (kJ) 
S 
Entropy (J/g K) 
T 
Temperature (K or ℃) 
W 
System positive work (kW) 
X 
Mass concentration (%) 
Subscript 

abs 
Absolute 
com 
Compressor 
eva 
Evaporator 
i 
Inlet 
o 
Outlet 
Tot 
Total 